Math Quizzes
What is the perimeter of the shaded portion of the figure?
$$68 \text{ in}$ To find the perimeter, add the perimeter of the outside with the perimeter of the inside. P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 \text{ in}P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 in
Which activity would best support kindergarten students in developing the ability to ask questions and seek answers through investigations?
Telling students that there is a problem with litter in the city and that the city planners would like a solution, and then guiding students into asking questions about the problem and suggesting ways to test solutions. This inquiry-based activity is tied directly to the learning goal. Students would be learning what makes a testable question.
The ΔABC in the coordinate plane will be translated 3 units to the right and then 4 units down. Which of the following points correctly expresses the location of vertex C after the translations?
(-2, -2) The original coordinates of point C are (-5, 2). A translation to the right increases the first coordinate, in this case, by 3 units: -5 + 3 = -2. A translation down decreases the second coordinate, in this case, by 4 units: 2 - 4 = -2.
Triangle ABC has been plotted on a coordinate graph with the points A (-3, 1), B (-1, 3), and C (-1, 1). If the triangle is translated 5 units right and 2 units down, what are the new coordinates of point A?
(2, -1) A translation of a geometric figure moves the entire figure to a new location in the same coordinate plane. If the movement is a shift to the right, the x-coordinate (first coordinate) should be increased. If the movement includes a shift down, the y-coordinate (second coordinate) should be decreased. Therefore, if the point (-3, 1) is shifted 5 units to the right and 2 units down, the new point will be (-3 + 5, 1 - 2) = (2, -1).
In the image below, the area of the triangle is 1 unit2. What is the total area of the figure?
11 unit2 Dissecting the figure, it becomes apparent that each square consists of two triangles. The hexagon consists of 6 triangles. Therefore, the total area is 2 + 2 + 6 + 1 = 11 units2
How many edges does a rectangular prism have?
12 A rectangular prism has 12 edges.
The images below are similar triangles. Solve for the missing value, x.
12 Since the triangles are similar, this question is best solved by setting up a proportion: \frac{15}{20} = \frac{x}{16}2015=16x Solving leads to 20x = 24020x=240. This reduces to x = 12x=12
A rectangle has a length that is twice the size of its width. If the perimeter of the rectangle is 48 inches, what is the area of the rectangle in square inches?
128 in2 Since the length is twice the size of the width, the equation for the perimeter would be P=w+w+l+l=w+w_{}+2w+2wP=w+w+l+l=w+w+2w+2w. Since the perimeter is 48, 48=6w48=6w so the width is 8 and the length must be 16. The area would then be A=lw= \left( 16 \right) \left( 8 \right) =128A=lw=(16)(8)=128 in2.
Ms. Trask wants to create an authentic assessment to test her students about angles in triangles. Which of the following should she do first?
Look at the standards to determine what a meaningful task that students could complete to demonstrate their knowledge. Looking at the standards to design the assessment is a great first step.
Which activity would best support third-grade students in developing an understanding of the Solar System and the positions of the planets relative to the Sun?
Making a physical model showing the order of the planets and three properties of each planet. This inquiry-based activity is tied directly to the learning goal. Students would interact with the planetary positions and also note some distinguishing features for each planet.
What is the area of the shaded region?
34 in2 One way to find the area is to find the area of the large rectangle, then subtract the area that is cut out. A=A_{\text{large rectangle}}-A_{\text{ small rectangle}}=(11\times 8)-(9\times 6)=88-54=34\text{ in}^2A=Alarge rectangle−A small rectangle=(11×8)−(9×6)=88−54=34 in2 Similarly, the shape could be divided into 4 rectangles, then the areas can be added together. A=2A_{rectangle_{1}}+2A_{rectangle_{2}}=2(11\times 1)-2(6\times 1)=22+12=34\text{ in}^2A=2Arectangle1+2Arectangle2=2(11×1)−2(6×1)=22+12=34 in2.
There are 9 regular parallelograms that compose a single large one. If the perimeter of each of the regular parallelograms is 14, what is the perimeter of the large figure?
42 If the perimeter is 14 then each side is 3.5 (14 ÷ 4 = 3.5). There are 12 sides used to compose the larger parallelogram. 12 × 3.5 = 42
What is the perimeter of the figure provided?
48 cm To find the perimeter, add the lengths of all sides. Since the right side has a length of 88 and the square cutout has side lengths of 44, the left edges must have a combined length of 44. P=8+12+4+4+4+4+12=48 \text{ cm}P=8+12+4+4+4+4+12=48 cm
What is the area of the figure provided?
49.5 cm2 The area of the figure is l × w = 5.5 × 9 = 49.5 \text{ cm}^2l×w=5.5×9=49.5 cm2.
How many faces does a square pyramid have?
5 A square pyramid has 5 faces. Remember that a pyramid only has one base.
A right triangle has one angle with a measure of 40 degrees. What is the measure of the other angle?
50 The sum of the interior angles of a triangle is always 180 degrees. Since the triangle is a right triangle, one measure is 90. The second angle is 40. 180 = 90 + 40 + x. Therefore, x must be 50 degrees.
How many faces does a rectangular prism have?
6 A rectangular prism has 6 faces.
What is the volume of the triangular prism pictured?
60 in3 The volume of a prism is in general B*h. The base of this prism is a triangle. The area of a triangle is ½ × b × h. The area of the base is ½ × 3 × 4 = 6 and then it is multiplied by the heights so 6 × 10 = 60.
A tennis ball has a diameter of about 3 inches. The container that holds a stack of three such balls is a right cylinder with a circular base. What is the approximate volume, in cubic inches, of the container that holds three tennis balls?
64 To find the volume of a right cylinder with a circular base, the area of the base of the cylinder is multiplied by its height. The area of the base of this container is a circle and so the calculation for its area should follow the formula A = πr2, where A = the area of the circular base and r = the radius of the base. The radius of the circular base of the can should be approximately equal to (though slightly larger than) the radius of the tennis ball. The diameter of the ball is given as "about 3 inches". Because diameter is twice radius, the radius of the tennis ball must be approximately half of that amount, or about 1.5 inches. Therefore, the area of the base of the cylindrical can with a circular base can be calculated as A = π(1.5)2 = 2.25π ≈ 7.07 square inches. It was given that the can for the tennis balls fits a stack of three tennis balls. Therefore, the height of the can should equal the height of three 3-inch diameter balls stacked on top of each other: 3(3 inches) = 9 inches. Therefore, the height of the can must be about 9 inches. Now the volume of the container can be calculated by multiplying the area of the circular base, ~7.07 inches, with the height of the can, ~9 inches. 7.07(9) = 63.63 in³. This answer can be rounded to approximately 64 cubic inches for the best approximate answer to this question.
The Huang family is building a circular swimming pool in their backyard with a diameter of 8 meters. They wish to place a decorative rock border along the edge of the pool from point A to point B, as shown by the dotted curve in the diagram. As seen in the diagram, points A and B are directly across from one another. Approximately how many linear meters of rock will be needed to form the decorative border along the edge of the pool from point A to point B?
12.6 m The length of the edge of the pool from point A to point B is a portion of the perimeter of the pool. Because points A and B are directly across from each other and the segment which connects them passes through the center of the circular swimming pool, the segment AB is a diameter, and so the portion of the perimeter of the pool that will have a decorative rock border is exactly half. Because the pool is in the shape of a circle, its perimeter is calculated using the formula for C, the circumference of a circle. C = πd. The circumference of the swimming pool is simply C = π×8 ≈ 3.14×8 ≈ 25.12 meters. Given that the circumference is ~25.12 meters, half that amount is 12.56 meters. Therefore, the best answer option is 12.6.
What is the total surface area of the figure provided?
132 in2 The total surface area is the surface area of all of the sides combined. The surface area of the two triangular bases is ½ × b × h = ½ × 3 × 4 = 6. There are two bases so their surface area is 12. There are three rectangular faces to the prism. 3 × 10 + 4 × 10 + 5 × 10 = 120. The sum of the lateral faces and the bases is 120 + 12 = 132 in2.
The cement pipe used in a storm drain system is an 8-foot long right circular cylinder with a wall thickness of 3 inches and an outside diameter of 24 inches. Which of the values below best approximates the volume, in cubic feet, of the interior of the pipe? (The formula for the volume, V, of a right circular cylinder with radius r and height h is V = πr2h.)
14.1 If the diameter of the pipe is 24 inches, then the radius of the pipe is 12 inches (because d = 2r, where d = diameter and r = radius). If the wall of the pipe has a thickness of 3 inches, then the interior of the pipe has a radius of 12 - 3 = 9 inches. Because the calculation is to be performed in cubic feet and not in inches, 9 inches must be converted to feet. This can be done using the conversion factor 1 foot/12 inches to cancel inches and bring in feet. 9 inches × 1 foot/12 inches = 9 feet/12, which reduces to ¾ feet, or 0.75 feet. Therefore, the radius to use in the volume calculation is 0.75 feet. The length of the cement pipe was given as 8 feet. Accordingly, the value to use as the height of the right circular cylinder is 8 feet. Finally, substitutions can be made and the appropriate calculations performed, using 3.14 as an approximation for π in the formula V = πr2h so that the volume of the interior of the pipe is discovered to be approximately 14.13 cubic feet. The best answer to select from the options, therefore, is 14.1. V = π(0.75)2(8)= π(0.5625)(8)= π(4.5)≈14.13 cubic feet
What is the volume of a ball that is 12 cm in diameter?
288π cm3 The volume of a sphere is equal to 4/3 × π × r3. Since the diameter of the ball is 12 cm, the radius of the ball is 6 cm. Therefore the volume of the sphere is equal to 4/3 × π × 63, which equals 288π cm3.
What is the perimeter of the figure provided?
29 cm The perimeter of the figure is 2 × (l + w) = 2 × (5.5 + 9) = 29 cm.
What is the area of the figure provided?
80 cm2 One way to find the area is to find the area of the large rectangle, then subtract the area that is cut out. A=A_{rectangle}-A_{square}=(12\times 8)-(4\times 4)=96-16=80 \text{ cm}^2A=Arectangle−Asquare=(12×8)−(4×4)=96−16=80 cm2. Another way to find the area is to separate the shape into rectangles, one large rectangle on the right and two smaller, congruent, rectangles on the left. A=A_{large rectangle}+2A_{small rectangle}=(8\times 8)+2(2\times 4)=64+16=80 \text{ cm}^2A=Alargerectangle+2Asmallrectangle=(8×8)+2(2×4)=64+16=80 cm2
The Trout family just purchased a large table in the shape of a perfect circle. It is 600 cm across. John helps set one side of the table for dinner and walks exactly halfway around the table. Which of the following is closest to how far has he walked?
950 cm Since John walked halfway around the table, we are solving for half of the circumference, C = 𝜋d. Since the table is 600 cm across, d = 600 cm and therefore P = 600𝜋cm. John walked halfway around, so John walked \frac{1}{2}(600)\pi21(600)π which is about 950 cm.
A student asks the teacher, "Why is the area of a triangle formula ½bh?" Which of the following would be the most appropriate answer for the teacher to provide
A parallelogram is the combination of two congruent triangles. Since the area of a parallelogram is bh, one half of the area of a parallelogram equals the area of a triangle. Every parallelogram is made up of two congruent triangles. The area for a parallelogram is base × height (bh), so the area of each of the two congruent triangles is one half of the parallelogram, or (1/2bh).
A teacher wants her students to demonstrate mastery of combining and dissecting figures. Which of the following is the best activity to determine if they have mastered this concept?
A project where students determine the area of 10 oddly shaped objects they have encountered in the last week and describe the process. This allows students to demonstrate mastery both in the objects they choose and their approach to determining the area. This also relates math concepts to the real world.
Mrs. Perkins is beginning to teach her class about congruent shapes. Which of the activities below is the best activity to introduce the subject?
Allow students to use cutouts of shapes that have been magnified to different dilations and compare and contrast their attributes. This teaches students at the concrete level since they are interacting with physical manipulatives. This is the best first activity.
Ms. Miles is teaching her students about circles. Students are having problems with determining area because many of them are confusing the formulas for circumference and area. What should she do to address the problem?
Create an activity where students determine area and circumference in a hands on way to activate a concrete level of understanding. A hands on activity will help students remember the formulas and how they are used in a meaningful way.
A fifth-grade teacher wants to assess students' ability to calculate the area of nonstandard polygons. Which of the following figures would assess a student's ability to find the area of non-standard polygons?
Figure 5 Figure 5 is a non-standard polygon because it does not have a standard geometric structure, such as a triangle, square, or rectangle do.
Mrs. Blue wants her students to be able to write two column geometric proofs. Which is the most appropriate way to determine their mastery?
Give students an open ended exam where they write multiple two column proofs. Asking students to write a proof is the best way to determine if they can write a proof.
A teacher wants to introduce her students to three dimensional figures. Which of the following is the best first activity to do?
Give students models of various three dimensional figures and have them write what they observe about the figures. Starting with something concrete that students can interact with will help them understand what three dimensional objects are.
A teacher is introducing the concept of volume to his fifth-grade class. Which of the follow is the best initial activity?
Give students several hollow objects and ask them which they think can hold more water and why they think that. Then allow them to determine the volume of water that fits inside each object. This is an engaging activity at the concrete level of learning.
A teacher wants his students to learn about different forms of energy in everyday life. Which of the following is the most engaging way to start a lesson that relates to the lesson goals and encourages students to see themselves as scientists?
Give students time to rotate through several hands-on science experiments that demonstrate the transformation of energy from one form to another. Not only does this pique interest in energy transformations, it also allows students to be scientists as they form theories and ideas about the different forms of energy present in the experiment.
Ms. Klein is teaching her students about tessellations. She brings in magnetic tiles for her students to create their own tessellations as an introductory activity. She hands them out to the students and then begins to explain the activity for the day. Students are not paying attention and instead building whatever they want. How can she improve her teaching practice?
Give the students clear instructions and a worksheet that accompanies the activity prior to handing out the tiles. It is vital to give out guidelines for use prior to handing out manipulatives.
After reading a story about a world that runs out of natural resources, a second-grade teacher wants students to think deeply about what they could do to prevent this in our world. Which of the following activities best supports critical thinking and relates to the lesson goal?
Have small groups of students discuss and evaluate their own thoughts about what they could do personally to conserve resources. This activity meets the lesson goals and requires students to think about their own lives, find connections, and evaluate the thoughts of others in their groups.
A third-grade teacher wants students to learn about the structures that help organisms survive within their environments. Which of the following activities best supports critical thinking and relates to the lesson goal?
Have students find similarities and differences in the breathing apparatus of fish, amphibians, and reptiles and connect their findings to life underwater versus life on land. This activity supports critical thinking by having students look for and find patterns, and it relates directly to the learning goal.
During a unit on Earth and space, Ms. Bosshardt wants her students to work on recognizing patterns by observing, describing, and illustrating clouds. Which of the following is the best way to incorporate technology into this lesson?
Have students go outside to observe clouds and use a phone camera to take pictures of a type of cloud that was previously discussed in the classroom. It is difficult to draw a cloud well enough to distinguish its type. By using a phone camera, students can observe real clouds and show with their photos that they understand different types of clouds.
A teacher wants students to understand how environments can support a population of plants and animals in an ecosystem. Which of the following is the most engaging way to start a lesson that relates to the lesson goals and encourages students to see themselves as scientists?
Have students observe and record the interactions of plants and animals in a terrarium over a span of several days or weeks. The interactions in a terrarium will best engage students by stimulating interest in the topic. It also allows students to be scientists by making, recording, and discussing their observations over a period of time.
Ms. Ludgate would like her students to participate in an Engagement activity for a unit on vascular and nonvascular plants. Which of the following is the most appropriate for an Engagement activity in the 5E Instructional Model?
Have students pair up, and give each pair a sample of a nonvascular plant and a vascular plant. Ask students to make observations and notice differences, then have each pair share their findings with the class. This activity does not require prior knowledge. It is an effective engagement activity.
During a unit on organisms and environments, Mr. Woodland wants his second-grade students to identify factors in the environment that affect plant growth. Students design investigations that involve growing bean plants in paper cups and exposing the plants to environmental variables of their choice. After the beans sprout, the students measure and record the heights of their bean plants. At the end of the investigation, students will be asked to present their data in a way that will be quick and easy to understand. Which of the following is the best way to incorporate technology into this lesson?
Have students record and graph their data in a spreadsheet that they can access each time they make a measurement. A spreadsheet is the best use of technology for this activity. It will allow students easy access to data that is collected over a period of time. Making a graph with a spreadsheet can be quick and students can experiment with different types of graphs and select the best graph for their presentation.
Which activity would best support first-grade students in developing an understanding of force and motion?
Have students use a ruler to push a low-friction object across their desks and describe the kind of push needed to make the object move in a straight line, in a zigzag pattern, and at different speeds. This inquiry-based activity is tied directly to the learning goal. Students would compare the strength and direction of the pushes needed to obtain each motion.
A third-grade class has been working on adding increments of time smaller than 60 minutes. The majority of students are able to correctly add 15- and 30-minute increments in both isolated problems and word problems. What activity could the teacher add to the next lesson to increase student engagement?
Have students work in pairs to create a new daily schedule with 30 more minutes of recess, 15 more minutes of lunch, and 15 more minutes of PE. This activity will encourage students to apply their knowledge to a familiar real-world scenario and will likely be an appropriate challenge for students to complete.
Which activity would best support third-grade students in developing an understanding of measuring with the metric system and creating graphs?
Having students use a metric ruler to measure the height of blades of grass growing in the schoolyard and then guiding them as they make bar graphs of their recorded results. This inquiry-based activity is tied directly to the learning goal. Students would measure, record, and graph metric data.
A child is using a geoboard and creates a shape with 6 sides. What is the name of this shape?
Hexagon A shape with 6 sides is called a hexagon.
A student is investigating the growth of Elodea under different light sources. Which of the following is the best research question for this student?
How does the type of light source affect the rate of photosynthesis of Elodea plants? This is the best and most testable research question.
Which of the following is a main benefit of using inquiry-based learning in the classroom?
Inquiry-based learning encourages students' scientific inquiry and develops their skills using the scientific method. Encouraging scientific inquiry and developing scientific method skills are main benefits of using inquiry-based learning.
A student performed an experiment on three different types of paper towels. Each of the towels was soaked in a separate beaker, each containing 20 ml of water, for exactly 15 seconds. The towels were removed. What step should be next in the procedure in order to accurately identify the paper towel that absorbed the most water?
Measure the remaining water in each of the three beakers and compare the results. To accurately compare the paper towel absorption, the amount of water remaining in each of the beakers must be measured and compared after removing the soaking paper towels.
Which of the following classroom activities is the best example of teaching inquiry-based science when learning basic anatomy?
dissection of a preserved frog in small groups Hands-on activities, which allow students to participate in the learning and apply acquired knowledge, have been proven to be the best method of science instruction.
Ms. Lemmons' class is about to carry out a lab experiment over plant growth. Which of the following would be the most effective way to carry out the experiment?
Ms. Lemmons can help the students form a hypothesis, identify their variables, and design an experiment before starting the experiment. By guiding the students in preparing for the lab, Ms. Lemmons will make the students feel more comfortable during the lab. Since students are writing their own labs, this will be more engaging.
As part of a lesson on electricity, Mrs. Garcia has her students complete the concept map shown here. If one student erroneously placed "lightening" in the box marked with an asterisk (*) and colored yellow, what is the best activity for Mrs. Garcia to do?
Partner that student with one that had this bubble correct and have them discuss and edit their maps. Lightning is a form of electricity, but not a source. This term should be in a bubble on the right hand side. By partnering with another student to discuss, the student can receive peer feedback.
Mr. Howard would like to create a short freewriting activity to determine whether his students are using critical-thinking skills on their current topic. Which Bloom's verb would be the best for him to use to start his prompt?
Predict Predicting is a higher level Bloom's verb which indicates critical thinking ability.
Which of the following terms best describes a polygon with 4 sides with only 2 angles of equal measure?
Quadrilateral A quadrilateral is a shape with 4 sides and 4 vertices. It can have any combination of equal angle measures.
What words describe the polygon below?
Regular and convex This heptagon is equiangular and all sides are congruent. It is also convex as all interior angles are less than 180°.
Mr. Barrios is teaching a unit on multiplication to his fifth-grade class. On the very first day he gives an exit slip with the following problem on it: 123.456 x 789 = _______ Every single student gets the question correct. How should he adjust his teaching?
Teach more advanced multiplication content to challenge his students. This is the best answer. While every student getting the answer to the exit correct could indicate stellar teaching, it could also indicate that students had previously mastered the material. He should consider adding more advanced content to his lessons to keep his students challenged and engaged.
As shown below, a figure was cut along the dotted line to form a second figure. What statement is true about the figures?
The area of the 2 figures is congruent, but the perimeter of the second figure is greater. The area is the same because the shapes occupy the same amount of space, but the perimeter is greater for the second figure because it has 2 new external lines where it was cut.
Billy and Sally perform the same experiment ten times to observe if variations occur in the results from the experiment. After they perform the experiment ten times, they notice a large variance of results, but they hypothesized a small variance in results. When they discuss the experiment with their teacher, the teacher directs them to identify any deviations from the original experimental procedure. Which of the following best describes the benefit of the teacher's directions?
The task helps Billy and Sally connect deviation in procedure to variance in results. By reviewing any deviations from the original experimental procedure, Billy and Sally can identify any procedures which might result in a large variance in the results of the experiment.
In which of the following assignments would students most likely find the Venn diagram to be a useful tool in organizing their information?
The teacher has asked the students to compare and contrast plants and animals. Venn diagrams are typically used when students are comparing and contrasting. The traditional Venn diagram has two circles that overlap. The area overlapping in the middle of the two circles is where you would record commonalities and the portions of the two circles outside of the overlapping area would contain the differences.
Use the figure below to answer the following question. Which of the following triangles is congruent with the triangle shown above
The three sides and the three angles of congruent triangles are exactly the same, although the triangles may have different orientations. In this case, the triangle has been rotated counterclockwise.
Many of today's education experts recommend that teachers move away from the "sage on the stage" approach and become more of a "facilitator of learning." What does this most likely mean?
This means that teachers need to move away from long lectures and move toward facilitating the classroom while allowing students to become active participants in learning. Today's educational leaders recommend that teachers move away from long lectures and give students more opportunities to become active participants in the classroom. Teachers need to become the "facilitator of learning" instead of being the person "doing the most learning". Lectures rarely involve students---the teacher is doing more learning than the students.
A child is using a geoboard and creates a shape with 3 angles. What is the name of this shape?
Triangle A triangle has 3 sides and 3 angles.
Which is the best way to help elementary students learn the scientific method?
Use ideas from the scientific method, with explicit instruction, in hands-on investigations throughout the year. Enabling students to repeatedly follow the scientific method, along with explicit instruction focusing on what they are doing and what they could do next, leads to real student understanding about the process of doing science.
Which of the following activities will best allow students to self-identify their misconceptions?
applying the scientific method to an idea in class and designing an experiment This method will best allow students to self-identify their misconceptions.
A student asks a teacher when would knowing the likelihood of a six being rolled on a dice be useful in real life. Which of the following examples would be the most appropriate response for the student?
a casino estimating the expected number of jackpot payouts over the next fiscal year Companies of chance (like casinos, insurance companies, etc) estimate the number of claims they will have to pay over the course of a given time period. This is a great example of probability and statistical analysis.
Which of the following best describes the polygon shown?
a convex pentagon A pentagon has 5 sides. A convex polygon has no angles greater than 180°. Another way to think of how to identify a convex pentagon is that it has no angles pointing inward.
Which of the following terms would be used to describe a polygon with six sides whose angles are all of equal measure?
a regular hexagon Since all angles are of equal measure, the polygon is regular. Since it has six sides it is a hexagon.
Which of the following students would qualify as an English-language learner?
a student whose family speaks Choctaw at home A student whose dominant language at home is any language other than English would qualify as an English-language learner.
Mr. Murphy is planning a lesson designed to meet the needs of all learners in his science class. The goal of his lesson is to help the learner enjoy learning science. Which of the following should Mr. Murphy incorporate first into the lesson in order to reach his goal?
activities focused on a variety of interests and learning styles In order for all students to enjoy the content, a variety of activities should be incorporated into the lesson. When these activities focus on the students' interests and learning styles, the students become more engaged in the lesson and enjoy learning.
A third-grade teacher is planning a lesson on representing data using dot plots. She plans to introduce the concept of dot plots, show examples, and create a class dot plot that shows how many siblings the students have. Which of the following would be the best way to incorporate technology into this lesson?
an online program that allows students to plot their data point on a dot plot Of the answer choices, this is the most effective use of technology because it involves student participation. By using an interactive online dot plot, the teacher is using technology for the most student-centered aspect of the lesson.
Which of the following steps in the scientific method is only completed after the experiment is completed?
communicating data After the experiment is concluded, the data is analyzed and then communicated.
Students have learned about the energy stored in rubber bands and springs and now use provided materials to build and test gum-drop launchers. Which phase of the 5E model is being implemented in this activity?
elaborate During the elaborate phase, students extend their thinking by applying what they have learned to a new situation and practicing new skills that were developed during the unit.
In a science center, students who stand in front of a wall when a light flashes will see a picture of their shadow on the wall afterward. Which phase of the 5E model is being implemented in this activity?
engage During the engage phase, students become mentally engaged and make connections to previous learning.
The 5E Model of Instruction is routinely recommended as one of the best practices in science classrooms. Which of these E's is generally the first step of the lesson cycle?
engage Engage is generally the first step of the lesson cycle if you are using the 5E Model of Instruction. (Engage, Explore, Explain, Elaborate, and Evaluate)
Technology is best utilized in the classroom when it can accomplish which of the following?
enhances the learning objective Technology is best used to enhance the learning objective of the lesson.
After learning about organisms and adaptations, a teacher asks students to describe what they learned about how a particular organism might survive during a drought. She finds that many of her students cannot think of any ways the organism might adapt. She decides she will extend the lesson to the next class period. Which phase of the 5E model is the teacher implementing when she asks for descriptions of adaptation?
evaluate During the evaluate phase, students demonstrate their understanding and teachers evaluate their learning to inform their next lesson.
Cara would like to research the effects of plants on students' self-reported stress levels. She places potted plants in student common areas for two weeks, taking surveys before and after. She then makes a graph of her findings. Which parts of the scientific method is Cara performing?
experimentation and data analysis Cara conducts an experiment (placing plants in common areas) and carries out data analysis (creating a graph of the results).
After observing the behavior of ants in an ant farm, students present their drawings and ideas about ant behavior to each other in small groups. Which phase of the 5E model is being implemented in this activity?
explain During the explain phase, students explain what they know and verbalize their understanding.
Elementary students use flashlights with opaque and transparent objects as they investigate shadows. Which phase of the 5E model is being implemented in this activity?
explore During the explore phase, students work with the materials to develop their knowledge. In this task, students manipulate materials and work to make sense of their findings.
Mr. Harris has several English-language learners in his classroom. He is currently beginning a unit about circuits. Which of the following activities will be most effective in engaging Mr. Harris' English-language learners in a lesson?
giving students bulbs, batteries, and connecting wires and asking them to try to make the bulbs light up Experimentation is one of the most engaging ways to start a lesson for English-language learners because it does not rely on their language skills. Later, Mr. Harris could help the students learn vocabulary associated with what they observed.
Mr. Fischer, a bilingual teacher, teaches a mathematics class composed of native English speakers and English language learners (ELLs). He has introduced a new topic with new vocabulary words in which he presented the vocabulary words with several examples. Which of the following strategies should Mr. Fischer use next to check each student's understanding of the vocabulary words?
having students write a definition for each term in their own words in their native language It is best to have the students construct their own definition in their native language so Mr. Fischer can assess their knowledge of the vocabulary words.
Which of the following activities best illustrates an activity related to using scientific inquiry in the classroom?
helping students identify a problem and develop testable questions that might lead to a solution An engaging part of scientific inquiry is allowing students to participate in the process of identifying problems to solve and asking questions that might lead to a solution.
Mr. Fielder has assigned students an open-ended research question for his fifth-grade science class. Which of the following should Mr. Fielder provide to ensure active engagement for his students in the activity?
inquiry-based instruction Inquiry-based instruction ensures students are active while learning.
In the figure, which line represents a line of symmetry?
line m Line m is the line of symmetry in this sketch. If you were to fold the figure on line m, the two halves would match up perfectly - much like the wings of a butterfly. One half would become a reflection of the other half when folded on m. This is not true of any of the other lines.
Which activity would best support second-grade students in developing an understanding of the stages in the life cycles of insects?
making and recording observations of a butterfly as it progresses from the egg stage to an adult butterfly while also using a chart to identify, name, and explain the stages This inquiry-based activity is tied directly to the learning goal. Students would compare their observations with the existing scientific understanding of the life cycle.
Which of the following is an inquiry-based activity that could be used during a unit on specific heat?
measuring and graphing temperature versus time for different materials placed under a heat lamp Conducting an investigation, measuring, and analyzing data develops student inquiry skills.
After reviewing a student's math assessment, the student's teacher has determined that the student is not following the order of operations when solving problems. Which of the following is the most appropriate remedial intervention?
mnemonic device Teaching the student to use a mnemonic device such as "PEMDAS" will help the student to recall which operations to solve first.
Of the following, which is most appropriate to do after testing a hypothesis?
organize data After testing a hypothesis it is best to organize the data so that conclusions can be drawn.
Which of the following activities best helps students practice the process skill of predicting?
participating in a discussion on which soil conditions might help plants grow taller after examining plants in the schoolyard A prediction is a guess based on observation. Participating in a discussion about what might happen with different soil conditions helps students develop prediction skills.
Which of the following cannot form a regular tessellation?
pentagon A regular tessellation must be able to tile a plane with no overlaps or gaps by repeating a regular polygon. The only regular polygons that can form a regular tessellation are the triangle, square, and hexagon. A regular pentagon does not form a regular tessellation.
According the 5E model, an ideal full lesson cycle should start by ___ and end with ___.
piquing students' interests; some sort of evaluation The full lesson cycle needs to start with an activity that piques students' interests and should end with an activity that evaluates what they have learned.
A second-grade teacher is planning to teach a lesson on measuring mass. What would be the best introductory activity for his students?
providing balance beam scales and various objects to compare This inquiry-based activity allows the students to explore the idea of weighing mass. The balance beam scale will easily show students which object is heavier.
Which terms best describe the triangle shown? Select all answers that apply.
right Right triangles contain a right (90 degree) angle. scalene Scalene triangles have all sides of different length.
Miguel is playing with his model cars. Which transformation is represented in the picture of his cars?
rotation This is a rotation because the top car has been rotated 180° about the point at the center, which is the transformation between the two cars, leaving you with this position and orientation of the bottom car.
Mrs. Campbell, a third-grade science teacher, is teaching conservation practices. What can her class do to demonstrate they have learned to make informed choices, based on the needs of the environment?
start a paper and plastic recycling program The best way to demonstrate that information was learned about conservation is to put the information into practice by recycling.
Traditionally, most elementary questions asked during instruction and assessment are at the recall level. Which level of Bloom's Taxonomy encourages the learner to think at the highest level?
synthesis (creating) The highest level of the hierarchy is synthesis (creating).
Mr. Shields is teaching a unit on magnetism with his third-grade students. Many have a misconception that all metals are attracted to magnets. Which of the following activities would most effectively help his students think critically about this statement?
testing magnetic attraction with a variety of metals One of the best ways for students to explore science, especially to disprove their misconceptions, is hands-on investigations. By giving them a variety of metals, some that will attract (ferromagnetic like iron) and others that won't (non-magnetic like copper), they can experience this difference first hand.
Which of the following is the best way to use data collected from pre-assessment activities?
to drive instruction Pre-assessing student knowledge helps the teacher focus the direction of the lesson where needed and adjust the pacing to meet the needs of the learners.
A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate. Which of the following did the student perform?
translation A translation is simply moving the object from one point on a plane to another point on the plane. The shape of the object remains the same; the object is simply moved along the plane.
At the end of a lesson on factoring, Ms. Wilson gave her class an exit ticket. After she reviewed the responses on the exit ticket, Ms. Wilson realized that many of her students were still struggling with the concept of factoring. Which of the following strategies would be best for Ms. Wilson to use in her next lesson on factoring to help the students solidify their conceptual understanding of factoring?
using manipulatives to show factoring as the reverse, or un-doing, of distribution This activity uses concrete manipulatives to demonstrate the concept of factoring. Students can use prior knowledge of distribution to make connections to factoring.
